Details

analyze1.5s (28.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	95.6%	4.4%	10
0%	95.2%	4.8%	11
0%	94.8%	5.2%	12
0%	92.4%	7.6%	13
0%	92.3%	7.7%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample2.1s (40.7%)

Results

1.0s	7587×	body	128	valid
751.0ms	1206×	body	8192	exit
91.0ms	258×	body	1024	valid
67.0ms	238×	body	512	valid
56.0ms	173×	body	256	valid
41.0ms	337×	body	128	invalid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify221.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

5304×	`fma-neg_binary64`
679×	`unsub-neg_binary64`
400×	`sub-neg_binary64`
376×	`fma-def_binary64`
289×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	23	14
2	59	14
3	157	12
4	438	12
5	1253	12
6	2078	12
7	2563	12
8	2777	12
9	2907	12
10	2949	12
11	2964	12
12	2967	12
13	2967	12
14	2967	12
15	3141	12
16	3015	12
17	3015	12
18	8062	12

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.6b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series13.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
2.0ms	(fma.f64 z -6 4)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

5.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
0.0ms	(fma.f64 z -6 4)

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-def_binary64`
445×	`associate-l_binary64`
416×	`exp-prod_binary64`
398×	`distribute-rgt-in_binary64`
387×	`associate-r_binary64`

Counts

68 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	1086
1	149	928
2	343	874
3	949	793
4	4177	793
5	4989	793
6	4976	793

prune51.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	44	5	49
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	7	51

Error

Counts

51 → 7

Alt Table

Status	Error	Program
	14.2b	(fma.f64 (-.f64 y x) (*.f64 (sqrt.f64 (fma.f64 z -6 4)) (sqrt.f64 (fma.f64 z -6 4))) x)
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.6b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	33.3b	(.f64 y (-.f64 4 (.f64 6 z)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 847 to 517 computations (39% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z -6 4)
✓	0.0b	(fma.f64 6 z -3)
✓	0.1b	(*.f64 y (fma.f64 z -6 4))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

series22.0ms (0.4%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
8.0ms	(*.f64 y (fma.f64 z -6 4))
2.0ms	(fma.f64 6 z -3)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 42

Calls

3 calls:

3.0ms	(*.f64 y (fma.f64 z -6 4))
0.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
0.0ms	(fma.f64 6 z -3)

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

798×	`neg-mul-1_binary64`
520×	`distribute-rgt-neg-out_binary64`
469×	`distribute-lft-neg-out_binary64`
296×	`fma-neg_binary64`
289×	`associate-l_binary64`

Counts

114 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1678
1	209	1387
2	553	1252
3	1824	1252
4	4279	1252
5	5516	1252

prune81.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	94	6	100

Error

Counts

100 → 6

Alt Table

Status	Error	Program
	0.6b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	17.7b	(fma.f64 x (fma.f64 6 z -3) (.f64 y (.f64 z -6)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
▶	0.1b	(fma.f64 x (-.f64 (.f64 6 z) 3) (.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 1661 to 1153 computations (30.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 6 z) 3)
	0.0b	(fma.f64 z -6 4)
	0.1b	(*.f64 y (fma.f64 z -6 4))
✓	0.1b	(fma.f64 x (-.f64 (.f64 6 z) 3) (.f64 y (fma.f64 z -6 4)))

series62.0ms (1.2%)

Counts

2 → 39

Calls

2 calls:

16.0ms	(fma.f64 x (-.f64 (.f64 6 z) 3) (.f64 y (fma.f64 z -6 4)))
2.0ms	(-.f64 (*.f64 6 z) 3)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(-.f64 (*.f64 6 z) 3)
0.0ms	(fma.f64 x (-.f64 (.f64 6 z) 3) (.f64 y (fma.f64 z -6 4)))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
574×	`associate-l_binary64`
554×	`fma-neg_binary64`
548×	`distribute-rgt-in_binary64`
534×	`distribute-lft-in_binary64`

Counts

69 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1132
1	235	981
2	496	844
3	1137	841
4	4587	841
5	4962	841

prune101.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	113	6	119

Error

Counts

119 → 6

Alt Table

Status	Error	Program
	0.6b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	17.7b	(fma.f64 x (-.f64 (.f64 6 z) 3) (.f64 y (*.f64 z -6)))
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.1b	(fma.f64 x (-.f64 (.f64 6 z) 3) (.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 2125 to 1529 computations (28% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
✓	0.0b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.2b	(.f64 6 (.f64 z x))
✓	0.3b	(.f64 6 (.f64 y z))

series37.0ms (0.7%)

Counts

4 → 18

Calls

4 calls:

21.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
8.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
5.0ms	(.f64 6 (.f64 y z))
4.0ms	(.f64 6 (.f64 z x))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-log-exp_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 93

Calls

4 calls:

12.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
4.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 y z))
4.0ms	(.f64 6 (.f64 z x))

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

443×	`times-frac_binary64`
372×	`cancel-sign-sub-inv_binary64`
279×	`associate-l_binary64`
278×	`distribute-rgt-neg-in_binary64`
271×	`associate-r_binary64`

Counts

111 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	2856
1	619	2159
2	2427	1906
3	4509	1906
4	5450	1906

prune134.0ms (2.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	148	6	154

Error

Counts

154 → 6

Alt Table

Status	Error	Program
	0.6b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	17.7b	(fma.f64 x (-.f64 (.f64 6 z) 3) (.f64 y (*.f64 z -6)))
✓	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.1b	(fma.f64 x (-.f64 (.f64 6 z) 3) (.f64 y (fma.f64 z -6 4)))

Compiler

Compiled 4889 to 2986 computations (38.9% saved)

regimes345.0ms (6.7%)

Accuracy

Total 0.2b remaining (92.5%)

Threshold costs 0.2b (92.5%)

Counts

68 → 1

Compiler

Compiled 5515 to 4082 computations (26% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	18	18
2	19	18
3	18	18

end99.0ms (1.9%)

Compiler: Compiled 148 to 104 computations (29.7% saved)

Details

analyze1.5s (28.3%)

sample2.1s (40.7%)

simplify221.0ms (4.3%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series13.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify87.0ms (1.7%)

prune51.0ms (1%)

localize9.0ms (0.2%)

series22.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify89.0ms (1.7%)

prune81.0ms (1.6%)

localize8.0ms (0.2%)

series62.0ms (1.2%)

rewrite4.0ms (0.1%)

simplify69.0ms (1.3%)

prune101.0ms (2%)

localize15.0ms (0.3%)

series37.0ms (0.7%)

rewrite28.0ms (0.5%)

simplify97.0ms (1.9%)

prune134.0ms (2.6%)

regimes345.0ms (6.7%)

simplify2.0ms (0%)

end99.0ms (1.9%)

Profiling